5. Use the angle addition formula to find the expression for cos (a+b).

Step-by-step explanation:

Trigonometric identities are used to show the equality of expressions involving trigonometric functions. These trigonometric functions are the sine, the cosine, and the tangent as well as their respective reciprocals which are cosecant, the secant, and the cotangent,

Some trigonometric identities are:

tanθ = sinθ / cosθ; secθ = 1 / cosθ; cosecθ = 1 / sinθ; cotθ = 1 / tanθ = cosθ / sinθ

The angle addition formula for cos is given as:

cos(α + β) = cosαcosβ - sinαsinβ

Therefore:

cos(a + b) = cosacosb - sinasinb

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15